Very good question. I want the answer too so I'll subscribe to this thread
I would guess you could just use the equation of a circle, (x - h)^2 + (y - k)^2 = r^2, h and k being the x and y coords of the center of the circle. With that you can solve for X or Y. From there you can determine the domain and range of the function to figure out which values to substitute.
Just a guess... I enjoy solving those sorts of problems, and I'm sure it'd be an interesting program to write. Hopefully someone who has done it before can give us a concise answer.